Medical radionuclide imaging or nuclear medicine is an important diagnostic tool for obtaining three-dimensional (3D) maps of the distribution of a radiation emission source administered to a patient. SPECT is a commonly used radionuclide imaging technique. Gamma radiation detectors are used to record the emission from the patient's body. This recorded data is used to reconstruct the 3D spatial distribution of the emission source in the patient's body. This reconstructed image is useful in the diagnosis of problems in different organs such as kidney, blood-vessels, heart, lungs, bone, and brain.
SPECT machines in prior art have relatively low sensitivity because they use a small aperture or small field-of-view collimator for gamma detectors. About 99% or more of the gamma photons carrying useful information are blocked and wasted by these small aperture/field-of-view collimators. As a result, Signal-to-Noise ratio in the gamma emission measurements are very low leading to poor quality in reconstructed tomographic images. Large field of view collimators are not used as they result in highly blurred images with depth/distance dependent blur of the radiation emission source and reduce the spatial resolution of reconstructed tomographic images. Large collimator apertures also increase errors due to increase in the sensing of scattered gamma rays which make the reconstructed tomographic images less accurate. These limitations of using a large aperture collimators are prevalent in the SPECT methods and apparatus in prior art but they are not as much in the novel SPECT method and apparatus disclosed here.
The theoretical foundation of the conventional SPECT method and apparatus is based on the following theoretical result: the tomographic reconstruction that provides the 3D spatial density distribution of a gamma emission source can be made from beam projection data, i.e. the measured values of the line-integral of the density of gamma emission source along different directions of view. Fourier-slice theorem states this result nicely for parallel projection data. See page 56 in the following book which is sold in book shops as well as freely available at www.slaney.org/pct:                A. C. Kak and Malcolm Slaney, Principles of Computerized Tomographic Imaging, Society of Industrial and Applied Mathematics, 2001. ISBN-10: 089871494X.        
In practice, integral/sum of the attenuated intensity of emission source elements along a thin line is measured. The thickness and shape of the elements' along the thin line in 3D space are determined by the collimator geometry, specifically the small aperture/field-of-view of the collimator. Attenuation of the emission is caused by the material substance around the emission source and through which the emission passes through before being measured. The measured line-integrals are called projection data or sinogram of attenuated emission. Projection data corresponding to different collimator structures such as parallel/converging/diverging-hole, fan-beam, cone-beam, etc., are used in prior art. However, all of this prior art is based on this theory of measuring and inverting line-integrals. When it becomes necessary to increase signal-to-noise ratio, i.e. increase sensitivity to information-carrying (non-scattered) gamma rays, the use of large apertures are forced by the rules of physics and geometry, and are accepted and used reluctantly. The distance/depth-dependent image blur of emission source caused by large apertures is treated as a serious undesirable problem. This depth dependent blur is reduced through one of several techniques that trade-off spatial resolution for errors due to noise in the reconstructed tomographic image. The gamma emission field is typically measured on a 2D planar surface that rotates around the emission source at a roughly constant/fixed distance/radius from an approximate center point of the emission source (see FIG. 3). The set of all points at which the emission field is measured forms a 3D surface with a small volume in the shape of a thin annular cylinder. In particular, this volume extends by a very small length along the radial dimension, but extends substantially much more along directions perpendicular to the radial distance.
A good description of conventional SPECT apparatus and method can be found in                1. P. C. Hawman, J. Qian; J. D. Treffert, “High-sensitivity SPECT imaging of small body organs using a multi-headscintillation camera with non-uniform collimation”, U.S. Pat. No. 5,462,056, Oct. 31, 1995.        2. G. T. Gulberg and G. L Zeng, “Three-dimensional SPECT reconstruction of combined cone-beam and fan-beam data”, U.S. Pat. No. 5,565,684, Oct. 15, 1996.A more recent development on a SPECT apparatus with a specially designed collimator structure that does not involve relative rotation between a patient and a gamma detector is reported in        E. G. Hawman, “Non-rotating transaxial radionuclide imaging”, U.S. Pat. No. 7,521,681 B2, Apr. 21, 2009,        
However, none of these include modeling and exploiting or measuring gamma radiation in a 3D measurement volume space that extends substantially along the radial direction. Therefore they have low sensitivity and the results are less reliable than the present invention. In prior art, SPECT/PET apparatus that measure gamma radiation at different angular positions tangential to a roughly circular contour around the object of interest is prevalent as the underlying theory for such apparatus is known to all persons skilled in the art. However, SPECT/PET apparatus that measure gamma radiation at different radial distances is not found anywhere except in the present invention. Such measurement along different radial distances was not considered in prior art perhaps because, based on intuition, it was assumed to provide no new information. There was no theoretical basis for such assumption as the new theory presented in here (Section 2.1, Eqs. 1.1 to 1.7) proves this assumption to be wrong.
Ohana et al (US 2010/0163736 A1) teaches a SPECT apparatus having a large collimator. However, Ohana et al's SPECT apparatus limits the motion of its gamma detector to orbit in a predetermined fixed radius orbit. The radius is fixed and the planar gamma detector moves tangentially to different angular positions similar to that shown in FIG. 3 here. The detector moves tangential to a roughly circular contour around the object of study but the detector does not move radially to different distances by moving farther and farther from the object of study. Therefore, the apparatus of Ohana et al does not capture essential information on the variation of gamma emission field along the radial direction that is needed for high-sensitivity 3D image reconstruction.